Question

10 use the diagram to answer the question below. suppose ( xm = 23x + -8 ) and ( my = 29x + -32 ) if ( overline{mn} ) bisects segment ( overline{xy} ), solve for ( overline{xy} ). ( xy = square )

Explanation:

Step1: Set \( XM = MY \) (bisector definition)

Since \( \overline{MN} \) bisects \( \overline{XY} \), \( XM = MY \). So, \( 23x - 8 = 29x - 32 \).

Step2: Solve for \( x \)

Subtract \( 23x \) from both sides: \( -8 = 6x - 32 \).
Add 32 to both sides: \( 24 = 6x \).
Divide by 6: \( x = 4 \).

Step3: Find \( XM \) and \( MY \)

Substitute \( x = 4 \) into \( XM \): \( 23(4) - 8 = 92 - 8 = 84 \).
\( MY \) is also 84 (since \( XM = MY \)).

Step4: Calculate \( XY \)

\( XY = XM + MY = 84 + 84 = 168 \).

Answer:

\( 168 \)